PHY-415

Welcome to the Relativistic Waves & Quantum Fields (PHY-415) Home Page

Course Organiser: Prof Gabriele Travaglini

Deputy Course Organiser: Dr David Berman

Marker:  Brenda Penante

 

Learning Outcomes

This course provides a first introduction into the unification of last century's groundshaking revolutions in physics: Special Relativity and Quantum Mechanics. Relativistic wave equations for particles of various spins are derived and studied, and the physical interpretations of their solutions are analyzed. Students will learn about the fundamental concepts of quantum field theory, starting with classical field theory, quantisation of the free Klein-Gordon and Dirac field and the derivation of the Feynman propagator. Then interactions are introduced and a systematic procedure to calculate scattering amplitudes using Feynman diagrams is derived. As an example, some explicit tree-level scattering amplitudes for a scalar theory are calculated. 

 

Syllabus

The syllabus will be updated during the course. MS stays for the book of Mandl and Shaw

Elements of Classical field theories: relativistic notation [MS Section 2.1, Section 1.2 of these notes], variational principle, equations of motion and Noether theorem [MS Section 2.2, part in Section 2.4]
 
Quantum Mechanics: Schroedinger equation, wavefunctions, operators/observables [revision, see your preferred QM book, Section 1.1 of these notes]; Schroedinger, Heisenberg and Interactions pictures [MS Appendix 1.5]. The Evolution operator [MS Sections 6.2]
 
Classical scalar fields: Klein-Gordon equation and action [MS Sections 3.1 and 3.2 (just the classical part), Section 2.1 of these notes]
 
Classical spinor fields: Dirac equation [MS Section 4.2 (just the classical part), Sections 2.2 and 2.7 of these notes], Gamma matrices [MS Section A.8, Sections 2.3 and 2.8 of these notes], relativstic properties of Dirac's equation [MS Section A.7 , Section 2.9 of these notes], an action principle for Dirac's field [MS Section 4.2 (just the classical part), Section 2.17 of these notes], plane wave solutions [MS Section A.4, Sections 2.10 of these notes], minimal coupling to an electromagnetic field [MS Section 4.5, Sections 2.20 of these notes], non-relativistic limit [Sections 2.21 of these notes]
 
Second quantization (free theories): Fock space for non-relativistic theories [optional, see for instance Sections 2.1-2.2 of "Quantum Field Theory" by L. S. Brown CUP], canonical quantisation and Fock space interpretation of the free complex and real Klein-Gordon field; normal ordering [MS Sections 3.1 and 3.2, see also these notes (be careful with the different conventions for the modes a(p)!)]. Causality, commutators and time ordered products, the Feynman propagator [MS Sections 3.3 and 3.4, see also these notes]

Interacting theories: natual units  [MS Sections 6.1], the evolution operator in the interaction picture and the S-matrix expansion  [MS Sections 6.2, see also these notes]. Tree level diagrams: an example for a scalar theory [see these notes].
 
Topics barely touched that will not be part of the exam, but that will be useful for the module Advanced Quantum Field theory: Fock space interpretation of the Dirac equation   [MS Sections 4.1 and 4.3], Dirac propagator  [MS Sections 4.4].

Schedule

Lectures will be held at University College in room UCL Physics, room to be confirmed, on Thursdays from 9:30am - 12:30pm.
First lecture: October 3, 2013.

If you do not know how to get to the classroom consult the Intercollegiate Physics MSci webpage.

Marking

Assessment for this course is based on a 10% contribution from the weekly exercises and 90% from the final examination in Semester 3.

Homework

During the semester eight homework assignments will be given. The homeworks will be posted on the webpage every Thursday and are due a week later (I collect them in the Thursday lecture). Late assignments will be marked to zero, unless you have medical or other valid reasons. Homework solutions will be available here a few days later.

Homework sheets

Week 1
Week 2 
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
 

Solutions

Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
 

References

A list of good books relevant for the course:
 
F. Mandl and G. Shaw, "Quantum Field Theory", J Wiley. (A pedagogical, clear book, the course will follow it as closely as possible. This book is also used in the 2nd term module Advanced Quantum Field Theory).
 
M.E. Peskin and D.V. Schroeder, "An Introduction to Quantum Field Theory", Addison-Wesley.
M Srednicki "Quantum Field Theory" Cambridge University Press.
(Very good books, which cover much more material than the course. If you are interested in theoretical particle physics and wish to study in more detail some topics or have a look at more advanced topic, choose one of these two references).
 
S. Weinberg, "The Quantum Theory of Fields" in 3 Volumes., Cambridge University Press. (Advanced book on Quantum Field Theory from a Nobel laureate. Probably overwhelming for a first QFT book. The first chapters of the first volume are relevant for the course.)
 
C. Itzykson and J.-B. Zuber, "Quantum Field Theory", (Another classic but less pedagogical than Peskin-Schroeder; in particular Sections 1, 2 & 3 have a lot of overlap with the course). 
 
J. Bjorken and S. Drell, "Relativistic quantum mechanics" and "Relativistic quantum fields", McGraw-Hill. (An old but reliable source, in particular the first book is relevant to the first part of my course).
 
There are also some detailed lecture notes by Andreas Brandhuber who gave this course in the past years: notes for the 2005 Relativistic Quantum Mechanics (RQM) , and the 2011 Relativistic Waves & Quantum Fields (part 1, part 2 and part 3).

Some of the past exam papers can be downloaded from here: 2012, 2011, 2010, 2009, 2008 and 2007.